Answer:
V ≈ 552.9 cm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height ) , then
V = π × 4² × 11 = π × 16 × 11 = 176π ≈ 552.9 cm³ ( to the nearest tenth )
Answer:
m=5
Step-by-step explanation:
We can solve this by using a system of equations. The easiest way to solve this is by using substitution.
3m=19-n Subtract both sides by 19 to find n.
<u>-19 -19</u>
3m-19=-n Divide everything by -1 to make n positive.
<u>/-1 /-1</u>
n=-3m+19
Now, we can substitute n into the second equation.
2m+5(-3m+19)=30 Substitute (-3m+19) into n.
2m-15m+95=30 Simplify.
-13m+95=30 Simplify and subtract both sides by 95.
<u>-95 -95</u>
-13m=-65 Divide both sides by -13.
<u>/-13 /-13</u>
m=5
We don't need to solve for n at all, so that is the answer!
Hope this helps, and have an amazing day ♥
Step-by-step explanation:
4t < 13
t < 13/4
I think this should be the answer
Part A)
f(x) = 5^x
f(0) = 5^0
f(0) = 1
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f(x) = 5^x
f(1) = 5^1
f(1) = 5
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f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
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f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125
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Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4
Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100
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Part B)
From part A) above, we found,
Rate of change for section A = 4
Rate of change for section B = 100
Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)
Answer for part B: 25
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Extra: Explain why one rate of change is greater than the other.
The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed.
Derivative Functions
The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. We can formally define a derivative function as follows.
Definition:
let f be a function. The derivative function, denoted by f', is the function whose domain consists of those values of x such that the following limit exists:
